Octave: Multiple submatrices from a matrix

Question

I have a large matrix from which I would like to gather a collection of submatrices. If my matrix is NxN and the submatrix size is MxM, I want to collect I=(N - M + 1)^2 submatrices. In other words I want one MxM submatrix for each element in the original matrix that can be in the top-left corner of such a matrix.

Here's the code I have:

for y = 1:I
    for x = 1:I
        index = (y - 1) * I + x;
        block_set(index) = big_mat(x:x+M-1, y:y+M-1)
    endfor
 endfor

The output if a) wrong, and b) implying there is something in the big_mat(x:x+M-1, y:y+M-1) expression that can get me what I want without needing the two for loops. Any help would be much appreciated

Answer 1

About your output being wrong, it might be because of the assignment. You're trying to assign a matrix to a vector position. Try using

block_set(:,:,index) = big_mat(x:x+M-1, y:y+M-1)

instead.

Answer 2

There seem to be a few things wrong in your code. Here's how I'd do it if I were to use the double loop:

M = someNumber;
N = size(big_mat,1); %# I assume big_mat is square here

%# you need different variables for maxCornerCoord and nSubMatrices (your I)
%# otherwise, you are going to index outside the image in the loops!
maxCornerCoord = N-M+1;
nSubMatrices = maxCornerCoord^2;

%# if you want a vector of submatrices, you have to use a cell array...
block_set = cell(nSubMatrices,1); 
%# ...or a M-by-M-by-nSubMatrices array...
block_set = zeros(M,M,nSubMatrices);
%# ...or a nSubMatrices-by-M^2 array
block_set = zeros(nSubMatrices,M^2);

for y = 1:maxCornerCoord
    for x = 1:maxCornerCoord
        index = (y - 1) * maxCornerCoord + x; 
        %# use this line if block_set is a cell array
        block_set{index} = big_mat(x:x+M-1, y:y+M-1);
        %# use this line if block_set is a M-by-M-by-nSubMatrices array
        block_set(:,:,index) = big_mat(x:x+M-1, y:y+M-1);
        %# use this line if block_set is a nSubMatrices-by-M^2 array
        block_set(index,:) = reshape(big_mat(x:x+M-1, y:y+M-1),1,M^2);
    endfor
 endfor

EDIT

I just saw that there is an implementation of im2col for Octave. Thus, you can rewrite the double-loop as

%# block_set is a M^2-by-nSubMatrices array
block_set = im2col(big_mat,[M,M],'sliding');

%# if you want, you can reshape the result to a M-by-M-by-nSubMatrices array
block_set = reshape(block_set,M,M,[]);

This is probably faster, and saves lots of digital trees.

Answer 3

With Mathematica: This code makes a matrix where each element is a matrix of MxM with each element in the original matrix in the top-left corner of such a matrix.

The matrix elements along the right and bottom are padded with x.

Partition[big_mat, {M, M}, {1, 1}, {1, 1}, x]

Example:

If you leave off x argument, then then it automatically samples periodically.